In systems designed for the digital transmission of images with as few bits as possible, noise from cameras and other sources not only degrades the image but also increases the number of bits required. Such systems generally operate by transmitting only the differences between successive frames, and since noise is usually random in nature, it adds to the difference.
One approach to noise reduction is the use of a frame averaging temporal pre-filter. In its simplest form, N adjacent frames of an image sequence are averaged together to form a frame in which the signal to noise ratio S/N is increased. This is due to the fact that noise is randomly distributed so that its average will be less than peak values whereas the average of a repetitious signal has the same values as the signal. Let f.sub.j be the input frames and f.sub.i be the frame averaged noise reduced frame, and (n.sub.1, n.sub.2) be the position within the block. Then, ##EQU1##
Usually k=(N-1)/2 but all that is necessary is that k.epsilon.[O, N]. If the input image sequence is static, i.e., has no motion, then this method results in the best possible noise reduction. Assuming zero-mean, stationary, white Gaussian noise, with N frames averaged together, a reduction in noise variance by a factor of N is achieved, see "Two Dimensional Signal and Image Processing" by J. Lim, (Prentice Hall, 1990, pp. 568-574.) specifically pages 568-9, which is incorporated by reference herein. If, however, the image is moving, applying simple frame averaging blurs the moving objects so as to reduce the image resolution.
The use of motion compensation with frame averaging can solve the problem of blurring. When motion compensation is used, N-1 motion compensated estimates of the reference frame under consideration are formed when N adjacent frames are to be used in the average. Then, these estimates, rather than the input frames, as in simple frame averaging, are averaged with the reference frame to form the noise reduced frame. If we let f.sub.j be the input frames, and f.sub.i be the motion compensated frame averaged noise reduced frames and g.sub.j,i be the motion compensated prediction of f.sub.i using f.sub.j, then, ##EQU2##
The motion compensated estimate can be formed by using block matching. The frames are divided into identical blocks. For each block in frame i, the closest matching block in each frame j is found. A common criterion to use in judging the closest match between two blocks is the mean absolute difference, MAD. Each block in the frame i is included in the average.
Moving objects in successive frames are well matched by this process so that the image resolution is retained. The best matches are achieved when small blocks are used. When, however, block matching is applied to a block that has little signal component and much noise, the matching block found matches the noise rather than the signal so that when frame averaging is performed, little noise reduction is achieved. Using large blocks makes it less likely that noise will be matched, but there may be poorer performance in signal matching. Thus, it is difficult to select an optimal block size.